Differentiability - AP® Maths Definition

What is differentiability in AP® Calculus?

Differentiability is a fundamental concept in calculus that describes whether a function has a derivative at each point in its domain. A function that is differentiable is smooth and has a well-defined tangent line at every point.

For a function to be differentiable at a particular point, it must first be continuous there; however, continuity alone does not guarantee differentiability. Key characteristics of differentiability include the absence of sharp corners or cusps and the lack of vertical tangent lines.

In the context of AP® Calculus, understanding differentiability is essential for mastering the computation and application of derivatives, as it allows students to analyse and predict the behaviour of various functions.

Differentiability study resources to ace your exams

Save My Exams has a great range of resources to help you explore the topic of differentiability in more detail. Try this study guide on the topic, then have a go at some multiple choice and free response exam questions.

Explore our Calculus AB and Calculus BC study resources.